Data update
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Ingy döt Net
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7735 changed files with 38060 additions and 199180 deletions
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@ -1,47 +0,0 @@
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with Ada.Text_IO; use Ada.Text_IO;
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with Ada.Complex_Text_IO; use Ada.Complex_Text_IO;
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with Ada.Numerics.Complex_Types; use Ada.Numerics.Complex_Types;
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with Ada.Numerics.Complex_Arrays; use Ada.Numerics.Complex_Arrays;
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procedure ConTrans is
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subtype CM is Complex_Matrix;
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S2O2 : constant Float := 0.7071067811865;
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procedure Print (mat : CM) is begin
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for row in mat'Range(1) loop for col in mat'Range(2) loop
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Put(mat(row,col), Exp=>0, Aft=>4);
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end loop; New_Line; end loop;
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end Print;
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function almostzero(mat : CM; tol : Float) return Boolean is begin
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for row in mat'Range(1) loop for col in mat'Range(2) loop
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if abs(mat(row,col)) > tol then return False; end if;
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end loop; end loop;
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return True;
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end almostzero;
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procedure Examine (mat : CM) is
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CT : CM := Conjugate (Transpose(mat));
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isherm, isnorm, isunit : Boolean;
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begin
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isherm := almostzero(mat-CT, 1.0e-6);
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isnorm := almostzero(mat*CT-CT*mat, 1.0e-6);
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isunit := almostzero(CT-Inverse(mat), 1.0e-6);
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Print(mat);
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Put_Line("Conjugate transpose:"); Print(CT);
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Put_Line("Hermitian?: " & isherm'Img);
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Put_Line("Normal?: " & isnorm'Img);
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Put_Line("Unitary?: " & isunit'Img);
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end Examine;
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hmat : CM := ((3.0+0.0*i, 2.0+1.0*i), (2.0-1.0*i, 1.0+0.0*i));
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nmat : CM := ((1.0+0.0*i, 1.0+0.0*i, 0.0+0.0*i),
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(0.0+0.0*i, 1.0+0.0*i, 1.0+0.0*i),
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(1.0+0.0*i, 0.0+0.0*i, 1.0+0.0*i));
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umat : CM := ((S2O2+0.0*i, S2O2+0.0*i, 0.0+0.0*i),
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(0.0+S2O2*i, 0.0-S2O2*i, 0.0+0.0*i),
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(0.0+0.0*i, 0.0+0.0*i, 0.0+1.0*i));
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begin
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Put_Line("hmat:"); Examine(hmat); New_Line;
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Put_Line("nmat:"); Examine(nmat); New_Line;
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Put_Line("umat:"); Examine(umat);
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end ConTrans;
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@ -1,76 +0,0 @@
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function conjugate-transpose($a) {
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$arr = @()
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if($a) {
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$n = $a.count - 1
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if(0 -lt $n) {
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$m = ($a | foreach {$_.count} | measure-object -Minimum).Minimum - 1
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if( 0 -le $m) {
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if (0 -lt $m) {
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$arr =@(0)*($m+1)
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foreach($i in 0..$m) {
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$arr[$i] = foreach($j in 0..$n) {@([System.Numerics.complex]::Conjugate($a[$j][$i]))}
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}
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} else {$arr = foreach($row in $a) {[System.Numerics.complex]::Conjugate($row[0])}}
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}
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} else {$arr = foreach($row in $a) {[System.Numerics.complex]::Conjugate($row[0])}}
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}
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$arr
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}
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function multarrays-complex($a, $b) {
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$c = @()
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if($a -and $b) {
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$n = $a.count - 1
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$m = $b[0].count - 1
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$c = @([System.Numerics.complex]::new(0,0))*($n+1)
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foreach ($i in 0..$n) {
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$c[$i] = foreach ($j in 0..$m) {
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[System.Numerics.complex]$sum = [System.Numerics.complex]::new(0,0)
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foreach ($k in 0..$n){$sum = [System.Numerics.complex]::Add($sum, ([System.Numerics.complex]::Multiply($a[$i][$k],$b[$k][$j])))}
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$sum
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}
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}
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}
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$c
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}
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function identity-complex($n) {
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if(0 -lt $n) {
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$array = @(0) * $n
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foreach ($i in 0..($n-1)) {
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$array[$i] = @([System.Numerics.complex]::new(0,0)) * $n
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$array[$i][$i] = [System.Numerics.complex]::new(1,0)
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}
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$array
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} else { @() }
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}
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function are-eq ($a,$b) { -not (Compare-Object $a $b -SyncWindow 0)}
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function show($a) {
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if($a) {
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0..($a.Count - 1) | foreach{ if($a[$_]){"$($a[$_])"}else{""} }
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}
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}
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function complex($a,$b) {[System.Numerics.complex]::new($a,$b)}
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$id2 = identity-complex 2
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$m = @(@((complex 2 7), (complex 9 -5)),@((complex 3 4), (complex 8 -6)))
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$hm = conjugate-transpose $m
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$mhm = multarrays-complex $m $hm
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$hmm = multarrays-complex $hm $m
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"`$m ="
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show $m
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""
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"`$hm = conjugate-transpose `$m ="
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show $hm
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""
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"`$m * `$hm ="
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show $mhm
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""
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"`$hm * `$m ="
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show $hmm
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""
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"Hermitian? `$m = $(are-eq $m $hm)"
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"Normal? `$m = $(are-eq $mhm $hmm)"
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"Unitary? `$m = $((are-eq $id2 $hmm) -and (are-eq $id2 $mhm))"
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@ -1,69 +1,39 @@
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conjugate_transpose<- function(M){
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t(Conj(M))}
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conj_t <- function(mat) t(Conj(mat))
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is_hermitian <- function(M,eps=10**-10){
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all(abs(M-conjugate_transpose(M))<eps)
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near_eq <- function(x, y, eps=10^-10) all(abs(x-y)<eps)
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is_hermitian <- function(mat) near_eq(mat, conj_t(mat))
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is_normal <- function(mat){
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mat_h <- conj_t(mat)
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near_eq(mat%*%mat_h, mat_h%*%mat)
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}
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is_normal <-function(M,eps=10**-10){
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conjugate <- conjugate_transpose(M)
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all(abs(M%*%conjugate- conjugate%*%M)<eps)
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is_unitary <- function(mat){
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id <- diag(nrow(mat))
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near_eq(mat%*%conj_t(mat), id)
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}
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is_unitary <-function(M,eps=10**-10){
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all(abs(M%*% conjugate_transpose(M)-diag(nrow(M)))<eps)
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mat1 <- matrix(c(3+0i, 2-1i, 2+1i, 1+0i), nrow=2)
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mat2 <- matrix(complex(real=c(1, 0, 1, 1, 1, 0, 0, 1, 1),
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imaginary=0),
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nrow=3)
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s <- sqrt(2)/2
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mat3 <- matrix(complex(real=c(s, 0, 0, s, rep(0, 5)),
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imaginary=c(0, -s, 0, 0, s, 0, 0, 0, 1)),
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nrow=3)
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conj_tests <- function(mat){
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cat("\nChosen matrix:\n")
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print(mat)
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cat("\nConjugate transpose:\n")
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print(conj_t(mat))
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test_funs <- c(is_hermitian, is_normal, is_unitary)
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results <- sapply(test_funs, function(f) f(mat))
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queries <- c("Hermitian?", "Normal?", "Unitary?")
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writeLines(paste(queries, results))
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}
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M1 = matrix(c(3+0i,2-1i,
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2+1i,1+0i),nrow=2)
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cat("M1")
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cat("\n")
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print(M1)
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cat("\n")
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Conj_M1 = conjugate_transpose(M1)
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cat("Conjugate transpose of M1")
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cat("\n")
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print(Conj_M1)
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cat(paste0("Hermitian ? ", is_hermitian(M1)))
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cat("\n")
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cat(paste0("Normal ? ", is_normal(M1)))
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cat("\n")
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cat(paste0("Unitary ? ", is_unitary(M1)))
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M2 = matrix(c(1+0i,0+0i,1+0i,
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1+0i,1+0i,0+0i,
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0+0i,1+0i,1+0i),nrow=3)
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cat("\n")
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cat("M2")
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cat("\n")
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print(M2)
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cat("\n")
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Conj_M2 = conjugate_transpose(M2)
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cat("Conjugate transpose of M2")
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cat("\n")
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print(Conj_M2)
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cat(paste0("Hermitian ? ", is_hermitian(M2)))
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cat("\n")
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cat(paste0("Normal ? ", is_normal(M2)))
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cat("\n")
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cat(paste0("Unitary ? ", is_unitary(M2)))
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M3 = matrix(c(sqrt(2)/2+0i,0-(sqrt(2)/2)*1i,0+0i,
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sqrt(2)/2+0i,0+(sqrt(2)/2)*1i,0+0i,
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0+0i,0+0i,0+1i),ncol=3)
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cat("\n")
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cat("M3")
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cat("\n")
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print(M3)
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cat("\n")
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Conj_M3 = conjugate_transpose(M3)
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cat("Conjugate transpose of M3")
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cat("\n")
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print(Conj_M3)
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cat(paste0("Hermitian ? ", is_hermitian(M3)))
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cat("\n")
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cat(paste0("Normal ? ", is_normal(M3)))
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cat("\n")
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cat(paste0("Unitary ? ", is_unitary(M3)))
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sapply(list(mat1, mat2, mat3), conj_tests) |> invisible()
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